# NSM Number Facts Principle 5

Developing an understanding of part whole relationships supports fluency in number facts.

## Research Finding

Experiences that focus on part-part-whole relations help students develop more efficient calculation strategies, especially for subtraction [13, 14, 15]. Numerate adults wouldn’t calculate 9-6 by counting back 6 from 9, however this is a strategy commonly used by children. If children are given experiences and teaching which help them learn that 9 breaks up into a 6 and a 3, then it becomes obvious that 9 – 6 = 3. Early teaching that emphasises these part whole relationships within single digit numbers leads to better understanding of quantity value, or the ‘fiveness’ of five. [16]

## Application to NSM Number Facts

NSM Number Facts Stage 1 and 2 provide extensive practice partitioning single digit numbers. Children spend time making and breaking all the numbers to 10 in great depth. This knowledge and skill is then explicitly called on in later stages of the programme, where children learn to solve calculations more efficiently by manipulating the numbers involved. The Make 10 and Then strategy, for example, teaches children to to add 8 +5 by calculating 8 + 2 + 3.

## References

[13] Armstrong, G. A.  (1991).  Use of the part-whole concept for teaching word problems to grade three children (Doctoral dissertation, National College of Education, 1990). Dissertation Abstracts International, 52(03), 833A.

[14] Huinker, D. M.  (1991).  Effects of instruction using part-whole concepts with one-step and two-step word problems in grade four (Doctoral dissertation University of Michigan, 1990).  Dissertation Abstracts International, 52(01), 103A.

[15] Rathmell, E., & Huinker, D.  (1989).  Using “part-whole” language to help children represent and solve word problems.  In P. R. Trafton (Ed.), New directions for elementary school mathematics (1989 Yearbook of the National Council of Teachers of Mathematics, pp. 99–110).  Reston, VA: NCTM.

[16] FISCHER, F. E. (1990), A part-part whole curriculum for teaching number in the kindergarten, Journal for Research in Mathematics Education, 21, 207–215.